The selection of the sample of massive cores was determined by the need of bright "standard'' sources for the SWAS satellite which has a spatial resolution of about 4 arcmin in the frequency range between 490 and 560 GHz. For a comparison to data obtained at similar angular resolution we used observations taken with the array receiver of the FCRAO 14 m telescope at 98 GHz (about 1 arcmin resolution) and performed complementary observations with the 3 m KOSMA telescope at 245 and 343 GHz where its beam size is approximately 2 arcmin.

The sources were selected from the SWAS source list (Goldsmith et al., priv. comm.) to be observable from the FCRAO and KOSMA and bright enough to be detectable in a reasonable integration time. Table 1 lists the 15 sources selected with their central position.

Table 1: Selected source sample with central positions.
Source $\alpha_{1950}$ $\delta_{1950}$

W49A ${19}^{\rm h}{07}^{\rm m}{50.0}^{\rm s}$ ${09}^{\circ}{01'}{32.0''}$

W33 ${18}^{\rm h}{11}^{\rm m}{19.8}^{\rm s}$ ${-17}^{\circ}{56'}{21.0''}$

W51A ${19}^{\rm h}{21}^{\rm m}{25.4}^{\rm s}$ ${14}^{\circ}{24'}{45.0''}$

W3(OH) ${2}^{\rm h}{23}^{\rm m}{15.4}^{\rm s}$ ${61}^{\circ}{38'}{53.0''}$

W3 ${2}^{\rm h}{21}^{\rm m}{42.5}^{\rm s}$ ${61}^{\circ}{52'}{22.0''}$

S255 ${6}^{\rm h}{09}^{\rm m}{58.4}^{\rm s}$ ${18}^{\circ}{00'}{19.0''}$

S235B ${5}^{\rm h}{37}^{\rm m}{31.8}^{\rm s}$ ${35}^{\circ}{40'}{18.0''}$

S106 ${20}^{\rm h}{25}^{\rm m}{39.8}^{\rm s}$ ${37}^{\circ}{12'}{46.0''}$

Serpens ${18}^{\rm h}{27}^{\rm m}{25.0}^{\rm s}$ ${01}^{\circ}{12'}{00.0''}$

DR21 ${20}^{\rm h}{37}^{\rm m}{14.0}^{\rm s}$ ${42}^{\circ}{09'}{00.0''}$

Mon R2 ${6}^{\rm h}{05}^{\rm m}{14.0}^{\rm s}$ ${-6}^{\circ}{23'}{00.0''}$

NGC 2264 ${6}^{\rm h}{38}^{\rm m}{26.0}^{\rm s}$ ${9}^{\circ}{32'}{00.0''}$

OMC-2 ${5}^{\rm h}{32}^{\rm m}{57.0}^{\rm s}$ ${-5}^{\circ}{12'}{12.0''}$

$\rho$ Oph A ${16}^{\rm h}{23}^{\rm m}{17.9}^{\rm s}$ ${-24}^{\circ}{17'}{18.0''}$

NGC 2024 ${5}^{\rm h}{39}^{\rm m}{12.0}^{\rm s}$ ${-1}^{\circ}{56'}{40.0''}$

**Table 1:** Selected source sample with central positions.
Source	$\alpha_{1950}$	$\delta_{1950}$
W49A	${19}^{\rm h}{07}^{\rm m}{50.0}^{\rm s}$	${09}^{\circ}{01'}{32.0''}$
W33	${18}^{\rm h}{11}^{\rm m}{19.8}^{\rm s}$	${-17}^{\circ}{56'}{21.0''}$
W51A	${19}^{\rm h}{21}^{\rm m}{25.4}^{\rm s}$	${14}^{\circ}{24'}{45.0''}$
W3(OH)	${2}^{\rm h}{23}^{\rm m}{15.4}^{\rm s}$	${61}^{\circ}{38'}{53.0''}$
W3	${2}^{\rm h}{21}^{\rm m}{42.5}^{\rm s}$	${61}^{\circ}{52'}{22.0''}$
S255	${6}^{\rm h}{09}^{\rm m}{58.4}^{\rm s}$	${18}^{\circ}{00'}{19.0''}$
S235B	${5}^{\rm h}{37}^{\rm m}{31.8}^{\rm s}$	${35}^{\circ}{40'}{18.0''}$
S106	${20}^{\rm h}{25}^{\rm m}{39.8}^{\rm s}$	${37}^{\circ}{12'}{46.0''}$
Serpens	${18}^{\rm h}{27}^{\rm m}{25.0}^{\rm s}$	${01}^{\circ}{12'}{00.0''}$
DR21	${20}^{\rm h}{37}^{\rm m}{14.0}^{\rm s}$	${42}^{\circ}{09'}{00.0''}$
Mon R2	${6}^{\rm h}{05}^{\rm m}{14.0}^{\rm s}$	${-6}^{\circ}{23'}{00.0''}$
NGC 2264	${6}^{\rm h}{38}^{\rm m}{26.0}^{\rm s}$	${9}^{\circ}{32'}{00.0''}$
OMC-2	${5}^{\rm h}{32}^{\rm m}{57.0}^{\rm s}$	${-5}^{\circ}{12'}{12.0''}$
$\rho$ Oph A	${16}^{\rm h}{23}^{\rm m}{17.9}^{\rm s}$	${-24}^{\circ}{17'}{18.0''}$
NGC 2024	${5}^{\rm h}{39}^{\rm m}{12.0}^{\rm s}$	${-1}^{\circ}{56'}{40.0''}$

NGC 2024 is not part of the SWAS sample but we have observed this region as a standard for comparison: it is relatively close ( $\approx$ 450 pc) and has been studied already by numerous authors using various techniques. An extended map of the cloud and its environment in CS 2-1 was provided by Lada et al. (1991), and line profiles in four transitions of the main CS isotope are given by Lada et al. (1997). Mezger et al. (1992) have identified seven clumps in NGC 2024 from dust observations using the IRAM 30 m telescope whereas the FCRAO and KOSMA beams can only distinguish between the two bright clumps FIR3 and FIR5. The data analysis is performed for the position of the brightest clump FIR5. Here, the KOSMA beam also contains weak contributions from FIR4, FIR6, and FIR7.

Table 2: Measured line parameters at the central core positions.
CS 2-1 CS 5-4 CS 7-6

Source $T_{\rm mb}$ $\int T_{\rm mb} {\rm d}v$ $\Delta v$ $T_{\rm mb}$ $\int T_{\rm mb} {\rm d}v$ $\Delta v$ $T_{\rm mb}$ $\int T_{\rm mb} {\rm d}v$ $\Delta v$

[K] [K kms^-1] [kms^-1] [K] [K kms^-1] [kms^-1] [K] [K kms^-1] [kms^-1]

W49A^(a) 3.77 35.17 8.75 $\pm$ 0.55 1.54 12.61 7.69 $\pm$ 0.19 1.23 12.15 9.28 $\pm$ 1.24

W49A^(b) 4.34 32.76 7.10 $\pm$ 0.38 2.04 18.70 8.62 $\pm$ 0.15 1.06 9.52 8.43 $\pm$ 1.03

W33 9.74 67.24 6.49 $\pm$ 0.16 3.76 27.40 6.84 $\pm$ 0.05 2.94 17.44 5.57 $\pm$ 0.05

W51A 10.86 110.51 9.56 $\pm$ 0.09 4.99 67.89 12.78 $\pm$ 0.09 3.38 40.63 11.28 $\pm$ 0.08

W3(OH) 5.50 26.48 4.53 $\pm$ 0.20 2.13 10.13 4.46 $\pm$ 0.08 1.25 5.81 4.40 $\pm$ 0.31

W3 7.67 38.97 4.77 $\pm$ 0.05 1.35 7.72 5.36 $\pm$ 0.28 1.56 8.44 5.08 $\pm$ 0.09

S255 8.02 21.55 2.53 $\pm$ 0.04 2.91 10.13 3.28 $\pm$ 0.03 1.67 5.29 2.99 $\pm$ 0.15

S235B 6.38 16.21 2.39 $\pm$ 0.05 0.85 2.67 2.97 $\pm$ 0.13 0.42 1.10 2.53 $\pm$ 0.19

S106 3.29 8.19 2.34 $\pm$ 0.10 0.83 2.11 2.40 $\pm$ 0.22 0.65 2.23 3.23 $\pm$ 0.78

Serpens 3.74 9.36 2.35 $\pm$ 0.13 0.67 2.52 3.59 $\pm$ 0.35 0.39 1.68 4.11 $\pm$ 0.65

DR21 6.48 25.00 3.62 $\pm$ 0.10 2.41 9.74 3.80 $\pm$ 0.18 2.92 10.92 3.51 $\pm$ 0.06

Mon R2 5.53 12.26 1.90 $\pm$ 0.16 2.15 6.52 2.38 $\pm$ 0.27 1.70 3.83 1.95 $\pm$ 0.19

NGC 2264 5.64 21.90 3.66 $\pm$ 0.08 2.30 9.48 3.89 $\pm$ 0.08 1.25 5.42 3.91 $\pm$ 0.12

OMC-2 5.62 9.26 1.55 $\pm$ 0.05 1.96 5.93 2.85 $\pm$ 0.10 0.92 1.54 1.58 $\pm$ 0.25

$\rho$ Oph A 4.22 11.10 2.47 $\pm$ 0.25 2.07 2.30 1.04 $\pm$ 0.08 <0.2 - -

**Table 2:** Measured line parameters at the central core positions.
	CS 2-1	CS 5-4	CS 7-6
Source	$T_{\rm mb}$	$\int T_{\rm mb} {\rm d}v$	$\Delta v$	$T_{\rm mb}$	$\int T_{\rm mb} {\rm d}v$	$\Delta v$	$T_{\rm mb}$	$\int T_{\rm mb} {\rm d}v$	$\Delta v$
	[K]	[K kms^-1]	[kms^-1]	[K]	[K kms^-1]	[kms^-1]	[K]	[K kms^-1]	[kms^-1]
W49A^(a)	3.77	35.17	8.75 $\pm$ 0.55	1.54	12.61	7.69 $\pm$ 0.19	1.23	12.15	9.28 $\pm$ 1.24
W49A^(b)	4.34	32.76	7.10 $\pm$ 0.38	2.04	18.70	8.62 $\pm$ 0.15	1.06	9.52	8.43 $\pm$ 1.03
W33	9.74	67.24	6.49 $\pm$ 0.16	3.76	27.40	6.84 $\pm$ 0.05	2.94	17.44	5.57 $\pm$ 0.05
W51A	10.86	110.51	9.56 $\pm$ 0.09	4.99	67.89	12.78 $\pm$ 0.09	3.38	40.63	11.28 $\pm$ 0.08
W3(OH)	5.50	26.48	4.53 $\pm$ 0.20	2.13	10.13	4.46 $\pm$ 0.08	1.25	5.81	4.40 $\pm$ 0.31
W3	7.67	38.97	4.77 $\pm$ 0.05	1.35	7.72	5.36 $\pm$ 0.28	1.56	8.44	5.08 $\pm$ 0.09
S255	8.02	21.55	2.53 $\pm$ 0.04	2.91	10.13	3.28 $\pm$ 0.03	1.67	5.29	2.99 $\pm$ 0.15
S235B	6.38	16.21	2.39 $\pm$ 0.05	0.85	2.67	2.97 $\pm$ 0.13	0.42	1.10	2.53 $\pm$ 0.19
S106	3.29	8.19	2.34 $\pm$ 0.10	0.83	2.11	2.40 $\pm$ 0.22	0.65	2.23	3.23 $\pm$ 0.78
Serpens	3.74	9.36	2.35 $\pm$ 0.13	0.67	2.52	3.59 $\pm$ 0.35	0.39	1.68	4.11 $\pm$ 0.65
DR21	6.48	25.00	3.62 $\pm$ 0.10	2.41	9.74	3.80 $\pm$ 0.18	2.92	10.92	3.51 $\pm$ 0.06
Mon R2	5.53	12.26	1.90 $\pm$ 0.16	2.15	6.52	2.38 $\pm$ 0.27	1.70	3.83	1.95 $\pm$ 0.19
NGC 2264	5.64	21.90	3.66 $\pm$ 0.08	2.30	9.48	3.89 $\pm$ 0.08	1.25	5.42	3.91 $\pm$ 0.12
OMC-2	5.62	9.26	1.55 $\pm$ 0.05	1.96	5.93	2.85 $\pm$ 0.10	0.92	1.54	1.58 $\pm$ 0.25
$\rho$ Oph A	4.22	11.10	2.47 $\pm$ 0.25	2.07	2.30	1.04 $\pm$ 0.08	<0.2	-	-

2.2 Observational details

All sources except NGC 2024 were observed in CS 2-1 by Howe (priv. comm.) using the FCRAO 14 m telescope providing a resolution of 53''. and a main beam efficiency $\eta_{\rm mb}^{2-1}=0.58$ . The cores were covered by 30-point maps with a sampling of 50''. The CS 2-1 spectra for the southern core in NGC 2024 were taken from Lada et al. (1997).

The CS 5-4 and 7-6 observations used the dual channel KOSMA SIS receiver with noise temperatures of about 95 K in the 230 GHz branch and 120 K in the 345 GHz branch. The 3 m telescope provides a spatial resolution of 110'' in CS 5-4 and 80'' in CS 7-6. The default observing mode for all cores were cross scans with a separation of 50'' between subsequent points. Only for NGC 2024 complete 5 $'\times$ 5' maps were obtained. At the time of the observations the telescope surface provided main beam efficiencies $\eta_{\rm mb}^{5-4}=0.54$ and $\eta_{\rm mb}^{7-6}=0.48$ respectively for the two transitions. For all measurements we use the conservative estimate of about 10% uncertainty for the main beam efficiency, another 10% atmospheric calibration uncertainty and add another 5% for possible drifts etc. As systematic errors they might sum up linearly to a total calibration error of at most 25%.

The FCRAO spectrometer had a channel width of 19.5 kHz corresponding to a velocity spacing of 0.060 kms^-1. For the broad lines from the sample four velocity channels were binned. The resulting rms falls between 0.2 and 0.45 K. The KOSMA spectra were taken with the medium resolution spectrometer (MRS) and the low resolution spectrometer (LRS) providing channel widths of 167 kHz and 688 kHz, respectively. Depending on the different combinations of these backends with the receivers at 245 and 343 GHz we obtain velocity spacings between 0.15 and 0.84 kms^-1. The particular spacing is not important for the analysis performed here because none of the lines shows strong spectral substructure. All points were integrated up to a noise limit of 0.1 K per channel.

2.3 Results

For most sources the CS 2-1 maps show an approximately elliptical intensity peak with a weak elongation at scales of a few times the resolution. In W49A, Serpens, DR21, Mon R2, OMC-2, $\rho$ Oph A, and NGC 2024 we can distinguish a second intensity maximum apart from the central position. Table 2 summarises the parameters of the line profiles at the central position for all cores. The majority of line profiles are approximately Gaussian as indicated by integrated line intensities close to the Gaussian value of $1.06\,T_{\rm mb}\Delta v$ in Table 2. Broad wings are only visible in S255, W33, and DR21.

W49 shows a double-peak structure which has been interpreted e.g. by Dickel & Auer (1994) as the footprint of large scale collapse. They fitted HCO⁺ line profiles by a spherical collapse model but concluded that additional components are needed to explain the observations. Using the radiative transfer code from Appendix B we have tested their infall model and found that, while reproducing the HCO⁺ profiles, it completely fails to explain the CS observations. The enhanced blue emission characteristic for collapse is visible only in CS 7-6. In CS 2-1 and 5-4 we rather find an enhanced red emission. No spherically symmetric collapse model can explain these observations. Instead of constructing a more complex model we have simply decomposed the emission into two separate components with a relative velocity of 8.5 kms^-1 in the line of sight denoted as W49A $^{\rm (a)}$ and W49A $^{\rm (b)}$ . From the modelling in Sect. 4 it turns out that we cannot even distinguish whether the two components are moving towards each other or apart as long as they do not line up exactly along the line of sight. Hence, we will treat them separately in the following, ignoring any possible interaction. Further observations including other tracers should be included to better resolve the situation.

Table 3: Measured line parameters within NGC 2024.
Transition $T_{\rm mb}$ $\int T_{\rm mb} {\rm d}v$ $\Delta v$

[K] [K kms^-1] [kms^-1]

C³²S 5-4 5.19 11.65 2.10 $\pm$ 0.02

C³²S 7-6 3.63 9.13 2.38 $\pm$ 0.08

C³⁴S 5-4 1.19 2.22 1.75 $\pm$ 0.09

C³⁴S 7-6 0.65 0.98 1.45 $\pm$ 0.13

**Table 3:** Measured line parameters within NGC 2024.
Transition	$T_{\rm mb}$	$\int T_{\rm mb} {\rm d}v$	$\Delta v$
	[K]	[K kms^-1]	[kms^-1]
C³²S 5-4	5.19	11.65	2.10 $\pm$ 0.02
C³²S 7-6	3.63	9.13	2.38 $\pm$ 0.08
C³⁴S 5-4	1.19	2.22	1.75 $\pm$ 0.09
C³⁴S 7-6	0.65	0.98	1.45 $\pm$ 0.13

In NGC 2024 we also mapped the less abundant isotope C³⁴S with KOSMA in addition to the main CS isotope observed in all cores. The observed line parameters are given in Table 3. Lada et al. (1997) provided detailed CS spectra for the southern core at the position of the FIR5. They obtained in the CS 2-1 transition $T_{\rm mb}=15.4$ K, $\Delta v=1.80$ kms^-1 at 24'' resolution, in CS 5-4 $T_{\rm mb}=9.6$ K, $\Delta v=2.1$ kms^-1 at 30''resolution, in CS 7-6 $T_{\rm mb}=10.1$ K, $\Delta v=2.7$ kms^-1at 20'' resolution, and in CS 10-9 $T_{\rm mb}=10.6$ K, $\Delta v=2.1$ kms^-1 at 14'' resolution.

2 Observations

2.1 The sample

2.2 Observational details

2.3 Results